More
about
Solving
C–1
File name 32sii-Manual-E-0424
Printed Date : 2003/4/24 Size : 17.7 x 25.2 cm
C
More about Solving
This appendix provides information about the SOLVE operation beyond that
given in chapter 7.
How SOLVE Finds a Root
SOLVE is an
iterative
operation; that is, it repetitively executes the specified
equation. The value returned by the equation is a function
f(x)
of the unknown
variable
x
. (
f(x)
is mathematical shorthand for a function defined in terms of
the unknown variable
x
.) SOLVE starts with an estimate for the unknown
variable,
x
, and refines that estimate with each successive execution of the
function,
f(x)
.
If any two successive estimates of the function
f(x)
have opposite signs, then
SOLVE presumes that the function
f(x)
crosses the
x
–axis in at least one place
between the two estimates. This interval is systematically narrowed until a root
is found.
For SOLVE to find a root, the root has to exist within the range of numbers of
the calculator, and the function must be mathematically defined where the
iterative search occurs. SOLVE always finds a root, provided one exists
(within the overflow bounds), if one or more of these conditions are met:
Two estimates yield
f(x)
values with opposite signs, and the function's
graph crosses the
x
–axis in at least one place between those estimates
(figure a, below).
f(x)
always increases or always decreases as
x
increases (figure b,
below).
The graph of
f(x)
is either concave everywhere or convex everywhere
(figure c, below).
